Re: Consciousness (was Re: From Atheism to Islam

2017-02-26 Thread Bruno Marchal

Hi Telmo!


On 25 Feb 2017, at 16:32, Telmo Menezes wrote:


Hi Bruno!

Evolution is a theory on the origins of biological complexity. We  
know

nothing about consciousness.




Do you agree that consciousness is a form of knowledge? That is:
consciousness requires some knowledge, and (genuine) knowledge  
requires some

conscious person)?


I agree, but I feel it begs the question: knowledge is an awareness of
something, it implies consciousness by definition.



it does not beg the question no more than the first order definition  
of the natural numbers beg the question, in the sense that you agree  
(or not) with the modal axioms for knowledgeable:


[]p -> p
[](p -> q) -> ([]p -> []q)

adding

[]p -> [][]p (for those having rich introspective knowledge)

Then, we can ask ourself what, in machine terms, or in machine+reality  
terms, would obey that theory. In this case, as you know, the  
Theaetetus idea works on Gödel's beweisbar predicate: the true  
opinion, or beweisbar and true [1]p = []p & p (makes [1] obeying the  
S4 logic above).


By Tarski, we cannot define "true" in the language of the machine, but  
we can model the knowledge by defining it on each (sigma_1  
arithmetical) p by beweisbar('p') & p. That provides a different  
logic, thanks to incompleteness, and indeed the arithmetically  
complete one (à-la Solovay) is axiomatized by an extension of S4: S4+  
Grz  (the formula []([](p->[]p) -> p) -> p from Grzegorczyk, a polish  
logician). (+ p -> []p to model the sigma_1 leaves of the universal  
dovetailer).


What is really nice here, is that the machine cannot name its first  
person self, and its metalogic reminds both Brouwer creative subject,  
but also the "inner god" of many eastern and western mystics. The soul  
of a machine is NOT a machine, nor anything third person describable,  
and It knows it.


Now, I could argue that consciousness per se is better modeled by  
[1]<1>p, but that is for the details (after all we do have distinct  
word for consciousness and knowledge, and a priori, consciousness  
might be delusional, where apparently, with the Theaetetic definition,  
it cannot be).





What is the situation with an artificial neural network?


Well, it will be harder for us to see its coded self, but it is Turing  
universal, and so can have one built by nature emulating Kleene's  
second recursion theorem through the neural net. The DNA strands did  
something like this already before (arguably).






Does it know
something, or is it akin to a stone being kicked down a hill?


The neural net knows nothing, but if the neural net embodies the right  
"codes" it might support a inner soul ([]p & p), like apparently our  
brains (which supports many souls which integrated well into the 1-I  
(hopefully, when sober).


I think that the left brain might be specialized in the 3p  
"analytical" believer []p (& <>t), and the right brain might be  
specialize with the intuitive, non definable "[]p & p (& <>t)".






Or is
the stone being kicked down a hill akin to our brains and requiring
consciousness already?


All relatively instanciated consciousness requires the universal  
consciousness of the non Löbian machine, I think, and get reflexive  
when Löbian, and inherit the Löbian theology, including its physics,  
making it testable (and its quantum logic seems to fit until now).







Then do you agree with the S4 theory of rational knowledge, which  
is that


(knowable x) implies x
(knowable (x implies y)) implies ((knowable x) implies (knowable y))
(knowable x) implies (knowable (knowable x))

With the inference rules:

If I prove x I can deduce (knowable x)
+ modus ponens


I'm ok with this.



OK.





If you are OK with this, it is not difficult to explain why  
evolution, or

anything actually, cannot NOT bring consciousness, and a first person
knower, in the picture.


Here I don't follow. Aren't you making the hidden assumption:

(knowable x) => (known x) ?



Only (knowable x) => (know x) on some leaves of the universal  
dovetailer.


Keep in mind that I live and work in Plato heaven, or Cantor paradise.  
I don't mind to wait any finite number of seconds. And the gal here is  
to figure out what is real, and what is "persistent illusion(s)", like  
Einstein qualified time.







Notice that I do tend to think what you say, that "anything actually,
cannot NOT bring consciousness" -- but I see this as part of my
"personal religion". I'm just not convinced that the above proves it.



It does not prove it, but follows from the mechanist assumption. Of  
course the theology of the (Löbian) machine does not need the  
mechanist assumption, except when we do the sigma_1 restriction, and  
get G1 and G1* and its intensional variants.







That is a consequence of incompleteness which make the machine  
aware of the
difference between []p and []p & p. The machine can know that []p  
obeys to

the modal logic G and that ([]p & p), the definition of "knowable" 

Re: Consciousness (was Re: From Atheism to Islam

2017-02-25 Thread spudboy100 via Everything List

This just my opinion, this, not being by necessity a permanent conclusion on my 
part, however, it seems to me that the conscious that we experience is 
basically, why the old philosophers called, material. Modern brain scientists 
would conclude in the type of brain cells, maybe Spindle Cells, their 
integration,and so forth that causes consciousness. There may be many other 
ways of developing or propagating consciousness. Simply, that it seems to me, 
that as it is currently known, its a biological thing. Yes, I am thinking it is 
not exclusively, bio, or what call, "carbon + water." I believe, unless there 
is a physical reason not to, that first "Weak AI," will be built, then, "Strong 
AI," which is like Marvin Minsky's 'guy in a box,' that we see interacting with 
people in all the sci fi stuff we see and read. Like Tony Stark's Jarvis, like 
HAL 9000 in 2001, aka as Minsky's 'guy in a box.' 


I am prejudiced in favor of much of the science fiction by astronomer, Alastair 
Reynolds, who does most of his stories limited by the absolute framework of 
relativity, and the sciences we know today.  So, without a reason to 
disbelieve, I am guessing that we will make AI of several flavors soon, and our 
great, great, great, great, grand kiddies will opt for a kind of mergence with 
these AI/machinery, for obvious reasons. One reason, would be that, as far as 
we know, it beats the heck out of dying early, especially if you like the idea 
of enlivening an apparently, dead milky way that is about us. I could be 
terribly, hugely wrong, spiritually, or psychologically, or cosmologically, 
but, its how I am rolling tonight. 


-Original Message-
From: Brent Meeker <meeke...@verizon.net>
To: everything-list <everything-list@googlegroups.com>
Sent: Sat, Feb 25, 2017 8:20 pm
Subject: Re: Consciousness (was Re: From Atheism to Islam





On 2/25/2017 11:06 AM, Telmo Menezes  wrote:


  


  
On Sat, 25 Feb 2017 at 18:17, John Clark <johnkcl...@gmail.com>
wrote:
  
  

  
On Sat, Feb 25, 2017 at10:32 AM, Telmo Menezes 
<te...@telmomenezes.com>wrote:




​>  ​
I always have a hard time seeing consciousness as   
 causal.



  


  

  
​Why, where is the  mystery? If external information didn't 
CAUSE your  consciousness to change you might as well be 
blind  and deaf, ​and if consciousness didn't CAUSE 
 external things to change you might as well be 
 paralyzed from the neck down . 
   
  

  
  

  
  
I meant and in the second sense. Take an artificialneural network 
driving a car. Like me, you suspect it mightbe conscious -- but we 
know the full mechanism. We know it'sa bunch of thresholds 
connected in a complex way, 

  


Of course if it's a big, deep neural network, even on simulated onvon 
Neumann architecture, that has been trained on a large range ofinstances 
(as it must be) we probably don't know how it's connectedand weighted and 
it would FAPP impossible to explain why it doeswhat it does in terms of its 
experience; and FAPP it would beimpossible to predict what it will do 
except by running it.  So itwill have "free" will. :-)

Brent
The sciences do not try to explain, they hardly even try to interpret, 
they mainly make models. By a model is meant a mathematical construct 
which, with the addition of certain verbal interpretations, describes 
observed phenomena. The justification of such a mathematical construct is 
solely and precisely that it is expected to work.
--—John von Neumann


  

  
running on von neumann machine and so on. How isconsciousness 
causing behavior ?
  

  
  

  


  

  
​  John K Clark ​
  


  



  


  

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Re: Consciousness (was Re: From Atheism to Islam

2017-02-25 Thread Brent Meeker



On 2/25/2017 11:06 AM, Telmo Menezes wrote:


On Sat, 25 Feb 2017 at 18:17, John Clark > wrote:


On Sat, Feb 25, 2017 at 10:32 AM, Telmo Menezes
> wrote:

​> ​
I always have a hard time seeing consciousness as causal.


​Why, where is the mystery? If external information didn't CAUSE
your consciousness to change you might as well be blind and deaf,
​and if consciousness didn't CAUSE external things to change you
might as well be paralyzed from the neck down .


I meant and in the second sense. Take an artificial neural network 
driving a car. Like me, you suspect it might be conscious -- but we 
know the full mechanism. We know it's a bunch of thresholds connected 
in a complex way,


Of course if it's a big, deep neural network, even on simulated on von 
Neumann architecture, that has been trained on a large range of 
instances (as it must be) we probably don't know how it's connected and 
weighted and it would FAPP impossible to explain why it does what it 
does in terms of its experience; and FAPP it would be impossible to 
predict what it will do except by running it.  So it will have "free" 
will. :-)


Brent
The sciences do not try to explain, they hardly even try to interpret, 
they mainly make models. By a model is meant a mathematical construct 
which, with the addition of certain verbal interpretations, describes 
observed phenomena. The justification of such a mathematical construct 
is solely and precisely that it is expected to work.

--—John von Neumann

running on von neumann machine and so on. How is consciousness causing 
behavior ?



​  John K Clark ​



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Re: Consciousness (was Re: From Atheism to Islam

2017-02-25 Thread John Clark
On Sat, Feb 25, 2017 Telmo Menezes  wrote:
​

> ​>> ​
>> ​Why, where is the mystery? If external information didn't CAUSE your
>> consciousness to change you might as well be blind and deaf, ​and if
>> consciousness didn't CAUSE external things to change you might as well be
>> paralyzed from the neck down .
>>
>>
>
> ​> ​
> I meant and in the second sense.
>

​I meant physical actions changing consciousness, what is the second
meaning? ​


> ​> ​
> Take an artificial neural network driving a car. Like me, you suspect it
> might be conscious
>

​Well... I suspect
a artificial neural network driving a car
​ is as
conscious as a typical human is ​who is driving over the same road he has
done a thousand times before, and that's not much. Can you remember one
specific event you were conscious of when you drove to work last Thursday?


> ​> ​
>  but we know the full mechanism. We know it's a bunch of thresholds
> connected in a complex way, running on von neumann machine and so on. How
> is consciousness causing behavior ?
>

​The problem is not unique to consciousness, how does anything "cause"
anything? When we say A causes Z we mean that whenever A happens Z happens.
But you could say that is mysterious because A is not Z, and indeed when we
look closer we discover that actually A causes B and then B causes Z, but B
is not Z either, and when we look even closer we find that B cause C and C
causes Z.  And so it goes. Either this chain of causality goes on forever,
in which case A doesn't cause Z at all and yet we know it does, or
eventually we come to a brute fact, Y causes Z and there is no "why" from
there.

But as I said this difficulty has nothing specifically to do with
consciousness, it's just in the nature of causality. If you are conscious
and if you are the product of random mutation and natural selection as
Darwin said them "intelligence causes consciousness" is a brute fact, but
eventually you'll always encounter a brute fact if you look at causal
chains close enough, not just ones involving consciousness.

John K Clark  ​










>
>
>> ​  John K Clark ​
>>
>>
>>
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Re: Consciousness (was Re: From Atheism to Islam

2017-02-25 Thread Telmo Menezes
On Sat, 25 Feb 2017 at 18:17, John Clark  wrote:

> On Sat, Feb 25, 2017 at 10:32 AM, Telmo Menezes 
> wrote:
>
> ​> ​
> I always have a hard time seeing consciousness as causal.
>
>
> ​Why, where is the mystery? If external information didn't CAUSE your
> consciousness to change you might as well be blind and deaf, ​and if
> consciousness didn't CAUSE external things to change you might as well be
> paralyzed from the neck down .
>
>

I meant and in the second sense. Take an artificial neural network driving
a car. Like me, you suspect it might be conscious -- but we know the full
mechanism. We know it's a bunch of thresholds connected in a complex way,
running on von neumann machine and so on. How is consciousness causing
behavior ?


> ​  John K Clark ​
>
>
>
> --
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> "Everything List" group.
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> email to everything-list+unsubscr...@googlegroups.com.
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Re: Consciousness (was Re: From Atheism to Islam

2017-02-25 Thread John Clark
On Sat, Feb 25, 2017 at 10:32 AM, Telmo Menezes 
wrote:

​> ​
> I always have a hard time seeing consciousness as causal.


​Why, where is the mystery? If external information didn't CAUSE your
consciousness to change you might as well be blind and deaf, ​and if
consciousness didn't CAUSE external things to change you might as well be
paralyzed from the neck down .


​  John K Clark ​

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Re: Consciousness (was Re: From Atheism to Islam

2017-02-25 Thread Telmo Menezes
Hi Bruno!

>> Evolution is a theory on the origins of biological complexity. We know
>> nothing about consciousness.
>
>
>
> Do you agree that consciousness is a form of knowledge? That is:
> consciousness requires some knowledge, and (genuine) knowledge requires some
> conscious person)?

I agree, but I feel it begs the question: knowledge is an awareness of
something, it implies consciousness by definition.

What is the situation with an artificial neural network? Does it know
something, or is it akin to a stone being kicked down a hill? Or is
the stone being kicked down a hill akin to our brains and requiring
consciousness already?

> Then do you agree with the S4 theory of rational knowledge, which is that
>
> (knowable x) implies x
> (knowable (x implies y)) implies ((knowable x) implies (knowable y))
> (knowable x) implies (knowable (knowable x))
>
> With the inference rules:
>
> If I prove x I can deduce (knowable x)
> + modus ponens

I'm ok with this.

> If you are OK with this, it is not difficult to explain why evolution, or
> anything actually, cannot NOT bring consciousness, and a first person
> knower, in the picture.

Here I don't follow. Aren't you making the hidden assumption:

(knowable x) => (known x) ?

Notice that I do tend to think what you say, that "anything actually,
cannot NOT bring consciousness" -- but I see this as part of my
"personal religion". I'm just not convinced that the above proves it.

> That is a consequence of incompleteness which make the machine aware of the
> difference between []p and []p & p. The machine can know that []p obeys to
> the modal logic G and that ([]p & p), the definition of "knowable" by
> Theaetetus, obeys to the modal logic S4 + Grz (with Grz the Gregorczyk
> formula).
>
> Now, consciousness is not exactly knowledge, but a knowledge of some
> "reality".

But "who" knows? Again, isn't this begging the question?

> It is based on an implicit automated belief in our consistency
> (which is equivalent with the existence of a "model" in the logician sense,
> which means some "reality" satisfying our belief. This makes consciousness
> close to inconsistency.

Interesting idea.

> Then it can be shown that consciousness, which is unavoidable, has still
> some important role in evolution, as it makes the machine self-speed-up-able
> and more and more autonomous relatively to the probable universal
> machine/number which supports them.

For me evolution has a very fractal-like quality to it, in the sense
that it generates machines that become very similar to the machine
where they come from. I am still not convinced that consciousness is
necessary to explain biological complexification. Can you expand?

> Similarly, we get the feeling and the qualia with the logic of []p a p, and
> []p & <>t & p, with p sigma_1. This add the symmetrical (p implies []p) in
> the picture, and leads to quantum sort of logics.

Here I don't follow. You alluded to this quantum-like logic a few
times but you never expanded (I think). I would be interested in a
more detailed explanation.

> It makes also consciousness into a bridge between the 3p arithmetical
> picture and the (many) 1p internal views, including the first person plural
> physics, making this theory testable (and confirmed up to now, both
> introspectively and quantitatively). cf NUMBER ==> CONSCIOUSNESS/DREAM ==>
> PHYSICAL-REALITY.

Do you believe you can make a prediction that could be experimentally
tested, ideally something that has not been observed yet?

> This explains notably why consciousness is what we know the best from the 1p
> view, and yet is completely NOT definable in any 3p sense (like the notion
> of Arithmetical Truth).

You mean because it does not exist in 3p?

> Intutively: consciousness brings the semantics, or the meaning of our
> beliefs, and that speed-up the possible actions of the machine, making the
> development of consciousness an advantage in the evolution, even if it
> brings some amount of self-delusion, like the many confusion between the
> reality that we infer with a reification of the reality that we observe ...
> until Pythagoras and Plato get back to the scientific doubt and skepticism.

I always have a hard time seeing consciousness as causal. What about
does experiments with MRI that show decision being made before the
person in aware of deciding?


T.

>>
 I don't quite understand why an omnipotent being

 would "want" anything, He should already have it.  Nevertheless the

 religious say God does want certain things and they know exactly
 precisely

 what they are and they insist on telling us about it; and they also
 insist

 God can't get what He wants on His own, we have to help the poor fellow

 achieve His aims.

>
 You are describing Abrahamic religions. I don't believe in them either.
>>>
>>>
>>>
>>> I don't think the
>>> Hindu religion
>>> is significantly less stupid. There are some forms of 

Re: Consciousness (was Re: From Atheism to Islam

2017-02-24 Thread Bruno Marchal


On 23 Feb 2017, at 21:12, Brent Meeker wrote:




On 2/23/2017 12:34 AM, Bruno Marchal wrote:


On 20 Feb 2017, at 16:33, Telmo Menezes wrote:

On Sat, Feb 18, 2017 at 1:19 AM, John Clark   
wrote:

On Wed, Feb 15, 2017 Telmo Menezes  wrote:





Dark Matter and Dark Energy remain complete mysteries.







As far as I can tell, what we have is a falsification of current
theories. They appear to be good enough approximations for many
things, but then they fail at predicting the expansion rate of the
universe right? Maybe it's dark matter, maybe it's something else,



They are 2 separate mysteries. Dark Matter is a mysterious  
something that
makes up 28% of the universe and holds galaxies and clusters of  
galaxies
together. Dark Energy is a even more mysterious something that  
makes up 69%
of everything and causes the expansion of the entire universe to  
accelerate.
And about 4% of the universe is made of the sort of normal matter  
and energy

that until about 20 years ago was the only type we thought existed.

There is a straightforward extension of General Relativity and  
Quantum
Mechanics that explains Dark Energy, however it gives a figure  
that is
10^120 too large, it's been called the worse mismatch between  
theory and
observation in the entire history of science. I think it's fair  
to say we
really don't have a clue about Dark Energy, and Dark Matter is  
almost as

confusing.




If science failed so far at explaining something, then it doesn't

matter?



Science has an explanation for consciousness that works  
beautifully,
consciousness is the way information feels when it is being  
processed

intelligently.


I know that your position is that information processing is
nonsensical without matter. Many times you invited Bruno to compete
with Intel, etc. So what you are saying is that "consciousness is  
the
way matter feels when it participates in an intelligent  
computation".

This "explanation" begs the question already.

Then there's the issue of defining "processed intelligently". What
does that even mean? Where do you draw the line between intelligent
and non-intelligent processing? Let me guess: intelligent processing
is the kind that generates consciousness.

Nobody ever came up with a way to test for the presence of
consciousness (probably because it's the wrong way to think about  
it),
so there is no scientific theory about it. Zero. You make it worse  
by

introducing ill-defined concepts.


What science doesn't yet have is a complete theory explaining
how to produce intelligence, but enormous progress has been made  
in just the

last few years.


Not really. What is happening is that the artificial neural network
models from the 80s are finally paying off, because of the orders of
magnitude more computational power and training data that we have  
now.


Progress is being made, but it has been very slow. It's a hard  
problem.


I've worked in this field both in academia and industry, for what  
it's worth.



The study of intelligence, now that's important!






That is a statement of faith. Gizmo worshiping.



At least 3 times a week for the last 5 years somebody on this  
list has
accused me of being religious, apparently in the hope that I'll  
burst into

tears and cry myself to sleep. It's not going to happen,


I can't talk for the others, but I have no interest in making you  
feel bad.

I'm just pointing out dogmatic thinking.






Yes, it's important in

a sense. I too am interested in having medical breakthroughs,  
freedom


from labour and all the nice things that AI can bring.



It's important even if you're only interested in philosophical  
problems,

such as why did Evolution bother to make conscious animals at all.


Evolution is a theory on the origins of biological complexity. We  
know

nothing about consciousness.



Do you agree that consciousness is a form of knowledge? That is:  
consciousness requires some knowledge, and (genuine) knowledge  
requires some conscious person)?


I don't think knowledge requires consciousness, much less a person.



Then we are talking about different things. Knowledge, in the sense of  
cognitive science, or epistemology, requires a knower, which is  
usually a person. Eventually, we need only to agree on the axioms, and  
propose variant.


In the context of describing "consciousness", it is seen as a  
particular "knowledge". (plausibly [1]<1>t)









Then do you agree with the S4 theory of rational knowledge, which  
is that


A theory of "knowable" is not the same as a theory of knowledge.  A  
theory of knowledge has to include the fact that much less is known  
than is knowable.


OK. It is the "omniscience problem". In the ideal context of the  
arithmetically self-referentially correct machine, this is handled by  
the difference between (x is a proof of y) and Ex(x is a prove of y).  
We can use this to have still different modal variant, like proving- 

Re: Consciousness (was Re: From Atheism to Islam

2017-02-23 Thread Brent Meeker



On 2/23/2017 12:34 AM, Bruno Marchal wrote:


On 20 Feb 2017, at 16:33, Telmo Menezes wrote:

On Sat, Feb 18, 2017 at 1:19 AM, John Clark  
wrote:

On Wed, Feb 15, 2017 Telmo Menezes  wrote:





Dark Matter and Dark Energy remain complete mysteries.







As far as I can tell, what we have is a falsification of current
theories. They appear to be good enough approximations for many
things, but then they fail at predicting the expansion rate of the
universe right? Maybe it's dark matter, maybe it's something else,



They are 2 separate mysteries. Dark Matter is a mysterious something 
that
makes up 28% of the universe and holds galaxies and clusters of 
galaxies
together. Dark Energy is a even more mysterious something that makes 
up 69%
of everything and causes the expansion of the entire universe to 
accelerate.
And about 4% of the universe is made of the sort of normal matter 
and energy

that until about 20 years ago was the only type we thought existed.

There is a straightforward extension of General Relativity and Quantum
Mechanics that explains Dark Energy, however it gives a figure that is
10^120 too large, it's been called the worse mismatch between theory 
and
observation in the entire history of science. I think it's fair to 
say we
really don't have a clue about Dark Energy, and Dark Matter is 
almost as

confusing.




If science failed so far at explaining something, then it doesn't

matter?



Science has an explanation for consciousness that works beautifully,
consciousness is the way information feels when it is being processed
intelligently.


I know that your position is that information processing is
nonsensical without matter. Many times you invited Bruno to compete
with Intel, etc. So what you are saying is that "consciousness is the
way matter feels when it participates in an intelligent computation".
This "explanation" begs the question already.

Then there's the issue of defining "processed intelligently". What
does that even mean? Where do you draw the line between intelligent
and non-intelligent processing? Let me guess: intelligent processing
is the kind that generates consciousness.

Nobody ever came up with a way to test for the presence of
consciousness (probably because it's the wrong way to think about it),
so there is no scientific theory about it. Zero. You make it worse by
introducing ill-defined concepts.


What science doesn't yet have is a complete theory explaining
how to produce intelligence, but enormous progress has been made in 
just the

last few years.


Not really. What is happening is that the artificial neural network
models from the 80s are finally paying off, because of the orders of
magnitude more computational power and training data that we have now.

Progress is being made, but it has been very slow. It's a hard problem.

I've worked in this field both in academia and industry, for what 
it's worth.



The study of intelligence, now that's important!






That is a statement of faith. Gizmo worshiping.



At least 3 times a week for the last 5 years somebody on this list has
accused me of being religious, apparently in the hope that I'll 
burst into

tears and cry myself to sleep. It's not going to happen,


I can't talk for the others, but I have no interest in making you 
feel bad.

I'm just pointing out dogmatic thinking.






Yes, it's important in

a sense. I too am interested in having medical breakthroughs, freedom

from labour and all the nice things that AI can bring.



It's important even if you're only interested in philosophical 
problems,

such as why did Evolution bother to make conscious animals at all.


Evolution is a theory on the origins of biological complexity. We know
nothing about consciousness.



Do you agree that consciousness is a form of knowledge? That is: 
consciousness requires some knowledge, and (genuine) knowledge 
requires some conscious person)?


I don't think knowledge requires consciousness, much less a person.



Then do you agree with the S4 theory of rational knowledge, which is that


A theory of "knowable" is not the same as a theory of knowledge.  A 
theory of knowledge has to include the fact that much less is known than 
is knowable.




(knowable x) implies x
(knowable (x implies y)) implies ((knowable x) implies (knowable y))
(knowable x) implies (knowable (knowable x))

With the inference rules:

If I prove x I can deduce (knowable x)
+ modus ponens


Proof is realtive to premises.  If you can prove x from true premises, 
THEN it's knowable.


Brent

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